纤维/树脂复合材料多尺度结构对力学性能的影响
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摘要
纤维增强树脂基复合材料具有较高的比强度和比模量、较强的可设计性、良好的抗疲劳性和耐腐蚀性以及便于整体成型等优点,已广泛用于航空航天、建筑、汽车、舰船、体育器材等领域。特别是在航空结构中,已成为主要材料之一。纤维复合材料具有内部结构多尺度化、组分材料高异质化的显著特征,导致力学性能与结构具有高度的关联性。因此,针对国家中长期科技发展规划中确立的大飞机重大专项,开展纤维复合材料的结构-力学性能相关性研究,实现高性能、低缺陷、低成本目标,具有重要的科学意义以及广阔的工程应用背景。
纺织结构复合材料和层合结构复合材料是航空工业中应用较广泛的两种工程结构件。纺织结构复合材料由于内部增强体交织构造的存在,其应力场高度非均匀化,在某些区域存在严重的应力集中,应力集中的位置与纺织构造和外载荷类型高度相关。层合结构复合材料在面内方向能够提供足够的承载能力,但由于层间区域界面性能较弱,对面外冲击高度敏感,容易造成层间分层,严重降低层合结构复合材料后继服役过程中的力学性能,形成潜在的安全隐患。解决上述问题的有效方法之一是开展纤维增强树脂基复合材料结构-性能相关性的数值分析,研究复合材料在各种载荷下的力学行为、损伤机理与内部结构之间的关联规律,为结构的优化设计提供理论基础与技术支持,使复合材料制品满足性能要求和尺寸要求,预测和避免潜在安全隐患的产生。尽管国内外已经开展了大量研究,但相对于复杂的物理过程,数值分析所建模型仍旧比较简化,同时缺乏不同材料结构之间的对比研究。针对这些不足之处,结合课题背景和项目来源,本文以纺织结构复合材料和层合结构复合材料为研究对象,采用数值分析的方法研究了材料结构对材料微观应力分布以及宏观力学响应的影响规律,同时在多尺度层次下对纤维复合材料结构-力学性能相关性开展了系统深入的研究。
本文的主要工作以及结论如下：
首先,针对复合材料多尺度结构中的微观尺度-纤维尺度,开展了单向复合材料力学性能的数值分析,并以此作为后续章节中纤维复合材料结构-性能相关性分析的基础。本文选取了更接近于横观各向同性的纤维六边形布排方式,建立了周期性代表单胞模型。在代表单胞的相对表面上施加了周期性边界条件,实现了材料受载变形之后其单胞对应边界上不仅位移连续而且应力连续,保证了结构的周期性和力学性能预测的准确性。针对纤维复合材料中存在的增强相、基体相以及界面相三种组分,分别采用横观各向同性(或者各向同性)、各向同性、内聚力模型等材料本构关系建立了相应的力学模型。数值模拟了单胞模型在多种载荷情况下的微观应力分布。同时,利用复合材料细观力学中的均质化方法分析了单向复合材料的等效弹性模量。在微观应力场分析的基础上,运用渐进损伤的方法,进一步针对单向复合材料的失效强度进行了有限元模拟,重点讨论了界面强度对单向复合材料整体失效的影响。结果表明：在纵向加载下,材料的失效强度由纤维主控,界面强度对纵向载荷下单向复合材料的失效行为影响较小；而在横向载荷下,基体损伤与界面失效交互出现,界面性能对材料整体失效有着重要影响,特别是在横向剪切载荷下,界面粘结强度的提高能够显著提高材料抵抗剪切失效的性能。
其次,在单向复合材料分析的基础上,针对更大结构尺度-纤维束尺度,数值分析了编织复合材料内部结构-力学性能相关性。以具有代表性的二轴编织复合材料(1×1编织和2×2编织)为研究对象,针对结构复杂、应力场分析困难、研究较少的非正交编织,本文摒弃了传统的矩形单胞选取方式,采用了更适于进行应力场分析的平行四边形周期性代表单胞；同时,考虑了非正交编织中纤维束变化的横截面,构建了更接近真实构造的有限元模型,在此基础上分析了不同纺织构造对复合材料弹性性能的影响以及在不同载荷情况下结构内部的非均匀应力分布规律,并进一步统计分析了材料内部的应力集中情况。研究发现：纺织结构复合材料内部的应力分布与纱线的交织构造具有高度的关联性；编织角对材料整体的等效性能具有重要影响；1×1与2×2这两个不同的编织构造之间的差异性同样会引起材料力学性能的不同。
然后,以单向纤维复合材料力学性能分析结论为基础,在宏观尺度上对层合结构复合材料的力学性能进行了数值分析。根据渐进损伤原理,针对层合结构复合材料在准静压下出现的各种损伤,确立了相应的失效判据和材料性能退化准则,构建了预测复合材料层合板准静压损伤的有限元模型,深入分析了在准静压载荷下层合板内部各种损伤的演化规律以及层合结构对准静压损伤的影响规律。研究结果表明：在冲击载荷下降之前,基体损伤以及分层破坏的扩展速度相对比较平缓,伴随材料宏观力学性能退化的出现,损伤开始快速扩展；在层合板总厚度不变的情况下,纤维铺层厚度的增加会加大层合板的基体开裂损伤以及分层损伤,同时抑制纤维断裂的发生。
最后,在复合材料层合板准静压损伤分析的基础上,进一步对层合结构复合材料在低速冲击下的力学响应进行了动态有限元分析。采用连续损伤力学构建了纤维铺层内的材料模型,运用内聚力模型构造了层间区域模型,将两者相结合建立了层合结构复合材料在低速冲击下的损伤有限元模型。深入分析了在低速冲击载荷下层合板整体的力学响应、分层损伤的演化过程、冲击能量转换耗散过程以及损伤区域分布规律,还讨论了层间界面性能以及纤维铺层角度对复合材料层合板低速冲击损伤的影响。通过分析损伤演化历程发现：冲击载荷首次下降与初始分层损伤的发生具有一致性；分层演化基本遵循先急后缓的规律；相对于法向分层,切向分层是层合结构复合材料受冲击过程中的主要分层模式；层间韧性的提高可以有效地减少低速冲击下的分层损伤面积；同时,在层合板内部设置更多的铺设角度会显著改进冲击损伤阻抗。
Fiber reinforced resin matrix composites have varieties of applications in aerospace, automobile, architecture and sports equipment industries because of their great performances, such as high specific strength and modulus, easy to design, good fatigue resistance and good corrosion resistance. Especially in aeronautical structures, composites have become one of the most important materials. Fiber composite material has an internal structure of multi-scaled and high heterogeneity of component materials, this results in that the mechanical properties of the fiber-reinforced composite material have a high degree of correlation with its structure. Aimed at the large aircraft development projects established by country mid-long-term scientific and technological development plan, research on the correlation between structure and property of fiber composite, to achieve high performance, low-defect, low-cost objectives, is of great practical significance.
Textile structural composites and laminated structural composites have been widely applied in the aerospace industry engineering structural components. Due to the textile structure of reinforcements in textile structural composites, the material internal stress field is highly non-homogenized and severe stress concentration exists in some regions. The position of the stress concentration is highly relevant to the type of textile structure and external load. The laminated structure composite materials can provide enough carrying capacity in the plane direction, but are highly sensitive to the out-plane load due to the weaker performance of the interface region between layers. Delamination is likely caused under the impact load seriously degrade the mechanical properties of laminated structural composites in the successor service process, forming a potential safety hazard. One of the effective ways to solve the above problems is to carry out the fiber reinforced resin matrix composite structure performance numerical analysis and study the correlation among the mechanical behavior, damage mechanism and the internal structure of the composite. This work is helpful for optimizing the structure design and can provide the theoretical basis and technical support for composite products which meet the performance requirements and size requirements, and predicting and avoiding potential safety hazards. Despite the large number of studies which have been carried out at home and abroad, compared with the complex physical processes, numerical analysis is still relatively simplified and lacks a comparative study between the different material structures. Against these deficiencies, combined with the subject background and project sources, this paper focused on textile structural composites and laminated composite. A numerical analysis method was used to study the effect of material organization structure on the material microscopic stress distribution as well as macro-mechanical response. At the same time, in the different structure levels, the correlation of structure and mechanical properties for fiber composite was further studied systematically. The main work and conclusions of this article are as follows:
Firstly, for the smallest structural scale in the multi-scale structure composite, fiber scale, the numerical analysis of the mechanical properties of unidirectional composites was carried out, which is the basis of the subsequent analysis on the bigger structural scale. A hexagonal array of fiber was adopted, which is closer to the transversely isotropic. A periodical representative unit cell model was presented with the periodic boundary conditions imposed on it, which ensures not only displacement continuity but also stress continuity in the corresponding boundary of unit cell. The enhanced phase, matrix phase and interface phase in composite were modeled through material constitutive of transversely isotropic(or isotropic), isotropic and cohesive zone model respectively. The microscopic stress distribution in composite under different loads was simulated through finite element model. The equivalent elastic modulus of unidirectional composites was analyzed through homogenization method of composite micromechanics. Based on the analysis of microscopic stress field, the failure strength of the unidirectional composite was predicted by the progressive damage method. The effect of the interface strength on the overall failure of unidirectional composite was discussed. It is shown that the property of fiber dominates the failure strength of the material under the longitudinal load, and the influence of interface strength can be ignored. Under transverse load, matrix damage and interface failure interactively appear, and interfacial properties have an important impact on the whole failure of the material, especially in the transverse shear loads. The improvement of the interfacial bond strength can significantly improve the performance of the material to resist shear failure.
Secondly, on the basis of analysis of unidirectional composites, for greater structural scale-fiber bundles scale, the correlation analysis on structure-properties of textile composites was carried out. This paper selected typical two-axis braided composites,1×1braid and2×2braid as the research object. Compared with the orthogonally braided composites, non-orthogonally braid composites have an irregular geometry configuration of fiber bundle, and the internal stress distribution analysis is more difficult. For non-orthogonally braided composites:the traditional rectangular unit cell was abandoned; a periodical parallelogram cell, more suitable for the analysis of the stress field, was adopted; and then the periodic boundary conditions were imposed. Taking into account the change in cross-sectional of the actual non-orthogonally braided fiber bundles, the finite element model, closer to the real configuration, was constructed. On this basis, the effect of textile structure on the elastic properties was discussed, as well as the stress distribution in the materials under different loads. Furthermore, statistical analysis of the stress concentration in the materials was carried out. It is found that the microscopic mechanical analysis is highly sensitive to the geometric architecture; the effect of braid angle on the mechanical properties is significant. The differences between1×1and2×2in effective elastic properties and stress distribution are caused by the structural differences:2×2has greater in-plane Young's modulus than1×1, the situation of the out-plane Young's modulus is on the contrary.
Thirdly, on the basis of conclusion of unidirectional fiber composites mechanics analysis, in the single ply scale, the mechanical properties of laminated composites were carried out. Starting from the indentation damage mechanics, the damage criterion and material performance degradation, corresponding to different damage in the composites under indentation load, were proposed. And a numerical model of laminated composites subjected to quasi-static indentation was established on the basis of progressive damage mechanics. The evolution of various damages within laminated structure under the quasi-static indentation was analyzed, as well as the effect of laminated structure on damage. It is found that the matrix damage and delamination propagate slowly before the first reduction of load, and then propagate quickly. Furthermore, under the condition of same laminates thickness, the effect of single ply thickness on the indentation damage was discussed. It is shown that the increase of single ply thickness can enlarge the matrix damage and the delamination degree, whereas it can restrain the development of fiber fracture.
Finally, on the basis of quasi-indention static analysis, the dynamic mechanical response of laminated composite under the low-speed impact was analyzed. The intra-ply damage including matrix crack and fiber fracture was represented by the continuum damage mechanics (CDM) which takes into account the physical progressive failure behavior in the ply, using the damage variable to describe the intra-ply damage state. The delamination at the interface between two plies was characterized by the cohesive zone model (CZM) which takes into account the normal crack and the tangent slip, using a specific correlation between traction and separation displacement to describe the initiation and development of delamination. A numerical method for the evaluation of composite laminates damage under the low-velocity impact was proposed by CDM and CZM. The correlation between the mesoscale structure and the macroscopic response under impact was constructed effectively by the finite element analysis. The effect of the interlaminar toughness on the impact damage was investigated, which is as yet seldom discussed in detail. The results reveal that as the fracture toughness enhances, the delamination area and the dissipated energy caused by delamination decrease. The contribution of different types of delamination is evaluated and the tangential slip is the dominant delamination during the impact process. Furthermore, the effect of ply orientation on the impact resistance was discussed. It is inferred that more orientation of fiber can make the impact resistance larger.
纺织结构复合材料和层合结构复合材料是航空工业中应用较广泛的两种工程结构件。纺织结构复合材料由于内部增强体交织构造的存在,其应力场高度非均匀化,在某些区域存在严重的应力集中,应力集中的位置与纺织构造和外载荷类型高度相关。层合结构复合材料在面内方向能够提供足够的承载能力,但由于层间区域界面性能较弱,对面外冲击高度敏感,容易造成层间分层,严重降低层合结构复合材料后继服役过程中的力学性能,形成潜在的安全隐患。解决上述问题的有效方法之一是开展纤维增强树脂基复合材料结构-性能相关性的数值分析,研究复合材料在各种载荷下的力学行为、损伤机理与内部结构之间的关联规律,为结构的优化设计提供理论基础与技术支持,使复合材料制品满足性能要求和尺寸要求,预测和避免潜在安全隐患的产生。尽管国内外已经开展了大量研究,但相对于复杂的物理过程,数值分析所建模型仍旧比较简化,同时缺乏不同材料结构之间的对比研究。针对这些不足之处,结合课题背景和项目来源,本文以纺织结构复合材料和层合结构复合材料为研究对象,采用数值分析的方法研究了材料结构对材料微观应力分布以及宏观力学响应的影响规律,同时在多尺度层次下对纤维复合材料结构-力学性能相关性开展了系统深入的研究。
本文的主要工作以及结论如下：
首先,针对复合材料多尺度结构中的微观尺度-纤维尺度,开展了单向复合材料力学性能的数值分析,并以此作为后续章节中纤维复合材料结构-性能相关性分析的基础。本文选取了更接近于横观各向同性的纤维六边形布排方式,建立了周期性代表单胞模型。在代表单胞的相对表面上施加了周期性边界条件,实现了材料受载变形之后其单胞对应边界上不仅位移连续而且应力连续,保证了结构的周期性和力学性能预测的准确性。针对纤维复合材料中存在的增强相、基体相以及界面相三种组分,分别采用横观各向同性(或者各向同性)、各向同性、内聚力模型等材料本构关系建立了相应的力学模型。数值模拟了单胞模型在多种载荷情况下的微观应力分布。同时,利用复合材料细观力学中的均质化方法分析了单向复合材料的等效弹性模量。在微观应力场分析的基础上,运用渐进损伤的方法,进一步针对单向复合材料的失效强度进行了有限元模拟,重点讨论了界面强度对单向复合材料整体失效的影响。结果表明：在纵向加载下,材料的失效强度由纤维主控,界面强度对纵向载荷下单向复合材料的失效行为影响较小；而在横向载荷下,基体损伤与界面失效交互出现,界面性能对材料整体失效有着重要影响,特别是在横向剪切载荷下,界面粘结强度的提高能够显著提高材料抵抗剪切失效的性能。
其次,在单向复合材料分析的基础上,针对更大结构尺度-纤维束尺度,数值分析了编织复合材料内部结构-力学性能相关性。以具有代表性的二轴编织复合材料(1×1编织和2×2编织)为研究对象,针对结构复杂、应力场分析困难、研究较少的非正交编织,本文摒弃了传统的矩形单胞选取方式,采用了更适于进行应力场分析的平行四边形周期性代表单胞；同时,考虑了非正交编织中纤维束变化的横截面,构建了更接近真实构造的有限元模型,在此基础上分析了不同纺织构造对复合材料弹性性能的影响以及在不同载荷情况下结构内部的非均匀应力分布规律,并进一步统计分析了材料内部的应力集中情况。研究发现：纺织结构复合材料内部的应力分布与纱线的交织构造具有高度的关联性；编织角对材料整体的等效性能具有重要影响；1×1与2×2这两个不同的编织构造之间的差异性同样会引起材料力学性能的不同。
然后,以单向纤维复合材料力学性能分析结论为基础,在宏观尺度上对层合结构复合材料的力学性能进行了数值分析。根据渐进损伤原理,针对层合结构复合材料在准静压下出现的各种损伤,确立了相应的失效判据和材料性能退化准则,构建了预测复合材料层合板准静压损伤的有限元模型,深入分析了在准静压载荷下层合板内部各种损伤的演化规律以及层合结构对准静压损伤的影响规律。研究结果表明：在冲击载荷下降之前,基体损伤以及分层破坏的扩展速度相对比较平缓,伴随材料宏观力学性能退化的出现,损伤开始快速扩展；在层合板总厚度不变的情况下,纤维铺层厚度的增加会加大层合板的基体开裂损伤以及分层损伤,同时抑制纤维断裂的发生。
最后,在复合材料层合板准静压损伤分析的基础上,进一步对层合结构复合材料在低速冲击下的力学响应进行了动态有限元分析。采用连续损伤力学构建了纤维铺层内的材料模型,运用内聚力模型构造了层间区域模型,将两者相结合建立了层合结构复合材料在低速冲击下的损伤有限元模型。深入分析了在低速冲击载荷下层合板整体的力学响应、分层损伤的演化过程、冲击能量转换耗散过程以及损伤区域分布规律,还讨论了层间界面性能以及纤维铺层角度对复合材料层合板低速冲击损伤的影响。通过分析损伤演化历程发现：冲击载荷首次下降与初始分层损伤的发生具有一致性；分层演化基本遵循先急后缓的规律；相对于法向分层,切向分层是层合结构复合材料受冲击过程中的主要分层模式；层间韧性的提高可以有效地减少低速冲击下的分层损伤面积；同时,在层合板内部设置更多的铺设角度会显著改进冲击损伤阻抗。
Fiber reinforced resin matrix composites have varieties of applications in aerospace, automobile, architecture and sports equipment industries because of their great performances, such as high specific strength and modulus, easy to design, good fatigue resistance and good corrosion resistance. Especially in aeronautical structures, composites have become one of the most important materials. Fiber composite material has an internal structure of multi-scaled and high heterogeneity of component materials, this results in that the mechanical properties of the fiber-reinforced composite material have a high degree of correlation with its structure. Aimed at the large aircraft development projects established by country mid-long-term scientific and technological development plan, research on the correlation between structure and property of fiber composite, to achieve high performance, low-defect, low-cost objectives, is of great practical significance.
Textile structural composites and laminated structural composites have been widely applied in the aerospace industry engineering structural components. Due to the textile structure of reinforcements in textile structural composites, the material internal stress field is highly non-homogenized and severe stress concentration exists in some regions. The position of the stress concentration is highly relevant to the type of textile structure and external load. The laminated structure composite materials can provide enough carrying capacity in the plane direction, but are highly sensitive to the out-plane load due to the weaker performance of the interface region between layers. Delamination is likely caused under the impact load seriously degrade the mechanical properties of laminated structural composites in the successor service process, forming a potential safety hazard. One of the effective ways to solve the above problems is to carry out the fiber reinforced resin matrix composite structure performance numerical analysis and study the correlation among the mechanical behavior, damage mechanism and the internal structure of the composite. This work is helpful for optimizing the structure design and can provide the theoretical basis and technical support for composite products which meet the performance requirements and size requirements, and predicting and avoiding potential safety hazards. Despite the large number of studies which have been carried out at home and abroad, compared with the complex physical processes, numerical analysis is still relatively simplified and lacks a comparative study between the different material structures. Against these deficiencies, combined with the subject background and project sources, this paper focused on textile structural composites and laminated composite. A numerical analysis method was used to study the effect of material organization structure on the material microscopic stress distribution as well as macro-mechanical response. At the same time, in the different structure levels, the correlation of structure and mechanical properties for fiber composite was further studied systematically. The main work and conclusions of this article are as follows:
Firstly, for the smallest structural scale in the multi-scale structure composite, fiber scale, the numerical analysis of the mechanical properties of unidirectional composites was carried out, which is the basis of the subsequent analysis on the bigger structural scale. A hexagonal array of fiber was adopted, which is closer to the transversely isotropic. A periodical representative unit cell model was presented with the periodic boundary conditions imposed on it, which ensures not only displacement continuity but also stress continuity in the corresponding boundary of unit cell. The enhanced phase, matrix phase and interface phase in composite were modeled through material constitutive of transversely isotropic(or isotropic), isotropic and cohesive zone model respectively. The microscopic stress distribution in composite under different loads was simulated through finite element model. The equivalent elastic modulus of unidirectional composites was analyzed through homogenization method of composite micromechanics. Based on the analysis of microscopic stress field, the failure strength of the unidirectional composite was predicted by the progressive damage method. The effect of the interface strength on the overall failure of unidirectional composite was discussed. It is shown that the property of fiber dominates the failure strength of the material under the longitudinal load, and the influence of interface strength can be ignored. Under transverse load, matrix damage and interface failure interactively appear, and interfacial properties have an important impact on the whole failure of the material, especially in the transverse shear loads. The improvement of the interfacial bond strength can significantly improve the performance of the material to resist shear failure.
Secondly, on the basis of analysis of unidirectional composites, for greater structural scale-fiber bundles scale, the correlation analysis on structure-properties of textile composites was carried out. This paper selected typical two-axis braided composites,1×1braid and2×2braid as the research object. Compared with the orthogonally braided composites, non-orthogonally braid composites have an irregular geometry configuration of fiber bundle, and the internal stress distribution analysis is more difficult. For non-orthogonally braided composites:the traditional rectangular unit cell was abandoned; a periodical parallelogram cell, more suitable for the analysis of the stress field, was adopted; and then the periodic boundary conditions were imposed. Taking into account the change in cross-sectional of the actual non-orthogonally braided fiber bundles, the finite element model, closer to the real configuration, was constructed. On this basis, the effect of textile structure on the elastic properties was discussed, as well as the stress distribution in the materials under different loads. Furthermore, statistical analysis of the stress concentration in the materials was carried out. It is found that the microscopic mechanical analysis is highly sensitive to the geometric architecture; the effect of braid angle on the mechanical properties is significant. The differences between1×1and2×2in effective elastic properties and stress distribution are caused by the structural differences:2×2has greater in-plane Young's modulus than1×1, the situation of the out-plane Young's modulus is on the contrary.
Thirdly, on the basis of conclusion of unidirectional fiber composites mechanics analysis, in the single ply scale, the mechanical properties of laminated composites were carried out. Starting from the indentation damage mechanics, the damage criterion and material performance degradation, corresponding to different damage in the composites under indentation load, were proposed. And a numerical model of laminated composites subjected to quasi-static indentation was established on the basis of progressive damage mechanics. The evolution of various damages within laminated structure under the quasi-static indentation was analyzed, as well as the effect of laminated structure on damage. It is found that the matrix damage and delamination propagate slowly before the first reduction of load, and then propagate quickly. Furthermore, under the condition of same laminates thickness, the effect of single ply thickness on the indentation damage was discussed. It is shown that the increase of single ply thickness can enlarge the matrix damage and the delamination degree, whereas it can restrain the development of fiber fracture.
Finally, on the basis of quasi-indention static analysis, the dynamic mechanical response of laminated composite under the low-speed impact was analyzed. The intra-ply damage including matrix crack and fiber fracture was represented by the continuum damage mechanics (CDM) which takes into account the physical progressive failure behavior in the ply, using the damage variable to describe the intra-ply damage state. The delamination at the interface between two plies was characterized by the cohesive zone model (CZM) which takes into account the normal crack and the tangent slip, using a specific correlation between traction and separation displacement to describe the initiation and development of delamination. A numerical method for the evaluation of composite laminates damage under the low-velocity impact was proposed by CDM and CZM. The correlation between the mesoscale structure and the macroscopic response under impact was constructed effectively by the finite element analysis. The effect of the interlaminar toughness on the impact damage was investigated, which is as yet seldom discussed in detail. The results reveal that as the fracture toughness enhances, the delamination area and the dissipated energy caused by delamination decrease. The contribution of different types of delamination is evaluated and the tangential slip is the dominant delamination during the impact process. Furthermore, the effect of ply orientation on the impact resistance was discussed. It is inferred that more orientation of fiber can make the impact resistance larger.
引文
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